What is the evidence ;n4nukcj2 ta:d3fe-ir0za -e that sound travels as a wave?

What is the evidence that sound is a form of enerqu5bg y n n).eq5 hv4ia1:re3agy?

Children sometimes play with a homemade “telephone” by attachin5t16m ntf 2l87x otzbgg a string to the bottoms of two paper cups. When the string is stre t1mxb 6otg t7fz8n25ltched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into watd+g:7rr vxbegphv,11a b 9ka0er, do you expect the frequency or wavd+gv19:ehb a, rva07 xp1 bgrkelength to change?

What evidence can you give thaur x7h n+d edi:yogv7gu1j2( *t the speed of sound in air does not depend significantly on frequency?dy 2j(7h7oi+g1eu*v:du gx nr

The voice of a person who has inhaled helium sounds very c n1y39r43zieb zz6xj high-pitched. Why?

How will the air temperature in a room m niwfd1 u,-zq auu,;8qs+,fk affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduct3dci . j*4zyge the amplitude of sounds indiyg*3c4tjz . various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog06ghztxgm5z+tz 6)w w ether as you move up the fzmwt06+6zgg x)th5 zwingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but iw1t3viczt)8cannot see it. When it emerges and yw 1)ziic3v8t tou do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in skm/txhu6,t4x5 nfn p*pace,” whereas beats can be said to be due to “interference ipu4nm x/5*,hxtnfkt6 n time.” Explain.

In Fig. 12–16, if the eub5ns-rte8 o(,pdtvo2a9: kfrequency of the speakers were lowered, would the points D and C (where destructive andtdp-9b2t8oo 5 seu:ek,r an (v constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work i* hg (iuz2xl y0i.y3h9w;cbdr as-2 din areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient nois 0uz9yw cix;s-2 b .32ldhr(hday*i ige. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each waq-i845q/,yi7xy1d bti vcpq y ve can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies fy, p-q 458dqq vy1c/ixtyi ib7arther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observkraoizl3mq2.i *ksdmi+ ( 3p -er move in the same direction, with the same velocity? Explain.ki (iliz q3*a2.kmpdsrm +3o-

If a wind is blowing,jrhj-r wb1)7k will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wav w )h17krr-bjjelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monito/u, 3odlvvcp :61xpn pr is blowing a whistle in front of the child on the ground. At ,xnvo p31/du:plp6cvwhich position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length 4v.6m;uf vz6zpluo 8r of a lake by listening for the echo of her shout reflected by a cliff lv8uv466op ;m.zu z frat the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hefm,b dxm6f8 )e hears the echo of the sound reflected from the ocean floor directly below 2.5 se6 f)bmd,m8fx later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air ajpr9rd5; ta. y;b/c/o5 ,v dbd0wylzht 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a schop++rg22d f cwo03e r0wl8s2jsr6ge l ool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is 28crl2rsg3dr+w wg+oo 0fseej0l62pheard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clifwg* ezxss94e79)i redf. The splash it makes when striking the water below is heard 3.5 s s*79z4 dsrix ee9)gewlater. How high is the cliff?    m

  A person, with his ear to the grou,/6cvsn2hb1 ba bkoa-- meu0couyxx+ 0e;t:wnd, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the airb,mo o/ a+b2txn cyu1 sa-:b 6x00-ehkc;wue v and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error mdw9rpj1hk:a w8gi g/lj4+ 5dcade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temper :d1l4pkij/jw ahdc8w5r+9 gg ature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? xjt+l ow 9 c (oi4r0+;pg3 3qlkq2dkhx   W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity62z;j;ne6 mh t cr*daja+mn j; is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ffr*d+ ensg x/x42jv 0j,r.sq at a certain place, what will +rj*v2 jg04, nsfxredqx/.sfbe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisymx x ./y/rvd-kaj*d i50 +zkea jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensitieej05. *a/dxk +zk/d aymvr -xis, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58m9hv6lkdl; ; ,* ommyf dB, whereas for a CD player it is 95 dB. What is the r; v,9;6 ykmflmom ldh*atio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking jw0- y;+t6fd ozacs wk-a/;soin normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mcow6;at fkyj+ z0sw;a/s-o d-outh. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose acj)uywz-2ol1 jd2 yp4z,f qe9rea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifi:acsf*c0n* p her B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeacpf s:**0 chanker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of 5pqsz7cd/ /(a do*t5oq gbs5ha loudspeak57p c shgo*qq(z5 o5adt// dsber on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound2qryp l(f egers8:: z9 level of 2.0 dB. What is the ratio of the amplitudes of two sounds w9z:8reyl qe rfg2: s(phose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a )8mf 9inah;bgsound wave is tripled, (a) by what factor will the intensity incb)f a98 ni;hgmrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ampli6epnqi)z jun qg*d 4 q/ca31:utudes, but one has twice the frequency of the other. What is the ratio of their i gp )nu3iucnjqd*a qzq/1e: 64ntensities?   

  What would be the sound level (in dB) of aonm,i1u s*0cf sound wave in air that corresponds to af0* ,n1iom usc displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to h dr/r1,9naabt:t( jw seem as loud as a 100-Hz tone that has a 50-dB sound level? (dwh: /a9n (,rar tbt1jSee Fig. 12–6.)    dB

What are the lowest and highest frequenci ndi+ k+ycyy3 2rrp9jiyr 6de+;+g1a jes that an ear can detect when the sound d2 ;kj+y 1 +y3reyajici9p n6 dy+rgr+level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range ofpbl2 o69ssib ) sound levels. What is the ratio of hii o9b2s6lpb)sghest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin h *ixwylfct;4 )as a fundamental frequency of 440 Hz. The length of the vibrating porfyi4wl)cx; t* tion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lonb,*n 12m;i ctt:wsi*w ud(zxug. What are the fundamental and first three audible overton;*scu* ,id wwtt1(u:n 2ix zbmes if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequenc t 5om4c3gg g7apl a;kc;-kyxd8xh,/zy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if 3hczx/y ,-mp;gdao 5tkgl8k 74axgc; you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning thb h;kt)k6sdf 3e range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes r3dthbfs6); kk equired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar strin ;(hnn4st6 j5gh(/zxafr 1 putg has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its origiz(ntjpta(6fg 5/h rnx1 hs;u4 nal length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovs 2x- ibp-ecm q,*w0g91 rrvcse middle C (33r0 qmp w12si,cx*9c-sb r g-ev0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262qrmv a581vylcqur y8g3;+4qv Hz) when the temperature is 21q1quvqag;vcr+84 lvym8y53r $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 20;wp .:j(9o oxes62:ubj4as:iublx o s $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–7c82 v rvqsc:c10 should the hole be that must be uncovered to play D above middle C at 8cccsr7qv:v 2 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 4d7xbl9yr snr*au3 8 b fp0.9fe40 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why t*a yl.8e0 bxrbu7p9r3n 9dffshis is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is ope;eek2oayiq *s(g 9r 8mn at both ends. It resonates at two successivs k g qemo8ie9r;(*2yae harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 i4ykc 6xz(wm9sr75-odh0o )d u r sk;a$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the f1r42b a e+vmoaudible range for a 2.14-m-long organ pim4vaof21 b+ repe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the ou io fig 74+*pn+.jxaoztside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in t+o+aofxz7i pn g4*. ijhe ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying xim 0x.q vs1wh33vu: uto adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other sthw:xm33s1q0vv . iuuxring? ±    Hz

  What is the beat frequency if middle C (262/o4afnn5e(+ o1 jyq rj:i uvi-d)kyd: Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 u/i x+ v;vrys54hr-odkHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency h;ri vo5uys v/d 4x-r+of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3l2av/sxe8.b ees iua 1d b8c fx:ft27850-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. f b.ebs:da8xl 182v/i2uf7 x 8eacetsWhat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hzptss8 ir/ :.yd. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eqisr8 pd:ty/s .. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to v krv1c0 th/meh/5.m mplay middle C (262 Hz), but one is at 5.0°C and the othe/m5mh0 hm tk1c/ vv.rer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. For+ rnw4nd4*us1r5kbmnbb3f+ 7y ej8 iuk B has a frequency of 441 Hz; when A and B are soundes1 enn mb+wn58yd 4fb3k 74b+juirur* d together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A pp45cx(p + g4atve 9rqp nvsy+)erson stands 3.00 m from one speaker and 3.50 m from the ott4pgy(p)+9vve4nsrp x+ 5caqher.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrat:nz: uy-g+veting at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are pluev -zt:n :yg+ayed together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wah fk 2c:sw34mgvmux) n n/wbe8t8g8y 7velengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assukhb388w /vf7n24utmgxg m:e nw)y s8cme T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fqc fqx5mc/ kw* (9ri7rd. ez3mire engine’s siren is 1550 Hz when at rest. Whamme ( kiq5rxfc/zc39*d 7qw.rt frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire enginenud70lq+7 u te whose siren emits at 1550 Hz moves at a speed of 32t0 7dnlu+e uq7 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving 3jjx4-fqau.x toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are jfja34 uq -x.xthey close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frv-7n + bl8yucb/s ajl,equency horn. When one is at rest and the other bluvls anj-/c +7,8yb is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50j05u 6 lm. znep(7a+ j9lr vreod/2fmm.0 kHz and receives them returned from an ob0vm6j92 /da m enpo.(erllrj 7u f+mz5ject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spaws* f 0y(ghf3 d7mpmazj6( *;lj)wyd eed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What freqm(p*dd; (j0 aaw*j lw m7zg6s3y y)hffuency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fl ( ,x(eyboy;qv.t f+wdat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approache . , q(voy(fbw;dtx+yed the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter usespi0vua3unnif 4q7/job6,d : m ultrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound sourn,qd :mi7a0nu ubf4povi6j3 /ce?   Hz

  The Doppler effect using ultrasonic waves of frequen za(gqxq 7;iw6pi3l re4qh7/vcy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequf32mg)jryy-kl-p1,l vu1 n dvency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hearyv1dl v-)y1-n2jrmu f3g pk l, who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if ity9k9,s gw r+ydk ;j 2j9v7gkb,7hxeibs speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels ph0n,n qj7; 9eqjn.ds at Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shoc , s9pe;jqn.j 7qhn0dnk wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the sppkc 9u3bdhuk1jo2 o4 ys2 zo*,eed of sound isok *j ou cdkys22ohbu1p,934z only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocelw 4 d,fds; hi7jvn3f5s:on-tan. Determine the shock wave angle it producejf -7s:d oln,dti3s;5h4nfw vs
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ptxx7o,3vi )p$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km aboveo9twhl2jb4(v6 s8wuc;/zx 8j rqi : ov the ground flying faster than the speed of sound. By theivl2 6qsxz/w4j vhj tc98o wu8(b: ro; time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends kncm u9 ;*gp(q20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum9mu* ;gpq( nkc depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audi; x;e jh57ej*lsgmoo4* j/hzgble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a hp:-d*g6uxn+2q hldl display called a sewer pipe symphony. It consists of many plastic pipes of various lengthshq*+lh-xl nd gud6 2:p, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close t : k -/nklp-rp111w:hyzasbm to the threshold of human hearing (0 dB). What will ba1rz: sbktwp1/-l hkmpn: -1 ye the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound levek zzzi /mwy+tm3b,i,/l when an 82-dB sound and an 87-dB sound are heazkiz,ti,zy3b+ m/wm /rd simultaneously?    dB

  The sound level 12.0 m from a loudsjh r8lf6p7 os .k syz bk6:m+,eezr1p;peaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direction6 s;.z 6yp71orbkjslhme+8efr p z:k,s?    W

  A stereo amplifier is rated at 150 1p.zv tdu5js7W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is7u5v1 t djszp. the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective de0 gzd*+g fsoa-;yiuy/:l xm tqv31.er vices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the averagstr xzfd:3uv-;il og e/a.m+y0*y1gq e human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, theevorjp8+kt :o+xbc;9 we1.v f gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned tozhk*r)hm0 ld1ak, g )d a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betweclcoj,*l;hri(elp ,aq 7, gt7c 8ric :en fixed points with a fundamental frequency of 440 Hz and a mass per unit le,c a:rhc,co r;llt (8 pii,g7c* q7eljngth of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertice.ymjb dl3-e;al open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the freque y.lj3b; e-medncy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is ophump ks(9mu3.3cwkdk6+j. h ken at one end and also 75 cm long. How much tension should hhk(k u6dus .mj+mk9p.ck3w3 be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onql ) 8)./ yko xkngnh:zs0f1(oer.ewpe full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming v j ;zqt7. ,:5,b8g;:ybyk esqott gbffrom two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency t ,5vgtsyz,jqykf:bb ;7;bqgo8e:t. is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor onn3 l;+fwtgfj+ the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the mov+fnj3w+gt ; lfing train?   m/s

  The frequency of a steam train whistle as it approa /(06epvw 8telnqx:8e) v pcyeches you is 538 Hz. After it passes you, its frequency is measured as 486 H(tc en/xqe8p0e: 8yl6vv ewp)z. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you c,cq q/f-e9qc dan estimate the speed of cars just by listening to the difference in pitch of the en,q -fceq /cq9dgine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat kd:3qg+ gl qtk(dh :i*frequency of 11 Hz. The shorter one is 2.40 m long. How long is the l+3gq:q*:kg t idhd(kother?    m

Two loudspeakers are at opposite ends of a railroad car as it moves w4s(m4rylzbd3c1w0z past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, 4031mw bz4crsy dlz(w in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blculxsb4(wjw1ye;or:y v.a8a0 .e 9 yv ood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume thatsayv;x ob jea lry:e8v.y 0c wu(94w.1 the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 2zakrg m s09fa;gu;vs *j7zh* 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat amruh9za as*s vz;7 gfkg0*2j; fter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pzj97c+s6ml -v8d2hf dpk ,iiyulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so th6y8i7 hdi j92dmkc -lzp,f v+sat the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used o: ;lzf ugpw(5to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn iuz5(pfw;: lgos about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by )opnu hju.3v/ the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the funduu3vo h.nj /)pamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lcg b i,jfmpk(n/-yn54ong, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, rip, ky ng-54/ijfmnbc(nging sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of-wy y2j ct)8eq about 1000 Hz is qet)cyy -8j 2w$I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2emi2x- upt-1 t.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. 2ximptt -eu 1-What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 +ipccrcnp fq/5.s: y6$^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h